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Some What-If Questions SENSITIVITY ANALYSIS

Uncertainty means that more things can happen than will happen. Therefore, whenever managers are given a cash- flow forecast, they try to determine what else might happen and the implications of those possible events. This is called sensitivity analysis.

Put yourself in the well-heeled shoes of the financial manager of the Finefodder supermarket chain. Finefodder is considering opening a new superstore in Gravenstein and your staff members have prepared the figures shown in Table 5.1. The figures are fairly typical for a new supermarket, except that to keep the example simple we have assumed no inflation. We have also assumed that the entire investment can be depreciated straight-line for tax purposes, we have neglected the working capital requirement, and we have ignored the fact that at the end of the 12 years you could sell off the land and buildings.

As an experienced financial manager, you recognize immediately that these cash flows constitute an annuity and therefore you calculate present value by multiplying the $780,000 cash flow by the 12-year annuity factor. If the cost of capital is 8 percent, present value is

PV = $780,000 АГАз 12-year annuity factor = $780,000 АГАз 7.536 = $5.878 million Subtract the initial investment of $5.4 million and you obtain a net present value of $478,000: NPV = PV investment = $5.878 million $5.4 million = $478,000

Before you agree to accept the project, however, you want to delve behind these forecasts and identify the key variables that will determine whether the project succeeds or fails.

Some of the costs of running a supermarket are fixed. For example, regardless of the level of output, you still have to heat and light the store and pay the store manager. These fixed costs are forecast to be $2 million per year.

Other costs vary with the level of sales. In particular, the lower the sales, the less food you need to buy. Also, if sales are lower than forecast, you can operate a lower number of checkouts and reduce the staff needed to restock the shelves. The new superstore`s variable costs are estimated at 81.25 percent of sales.

Thus variable costs = .8125 АГАз $16 million = $13 million.

The initial investment of $5.4 million will be depreciated on a straight-line basis over the 12-year period, resulting in annual depreciation of $450,000. Profits are taxed at a rate of 40 percent.

These seem to be the important things you need to know, but look out for things that may have been forgotten. Perhaps there will be delays in obtaining planning permission, or perhaps you will need to undertake costly landscaping. The greatest dangers often lie in these unknown unknowns, or БІАААмunk-unks,БІАААн as scientists call them.

Having found no unk-unks (no doubt you`ll find them later), you look at how NPV may be affected if you have made a wrong forecast of sales, costs, and so on. To do this, you first obtain optimistic and pessimistic estimates for the underlying variables. These are set out in the left-hand columns of Table 5.2.

Next you see what happens to NPV under the optimistic or pessimistic forecasts for each of these variables. You recalculate project NPV under these various forecasts to determine which variables are most critical to NPV.

Sensitivity Analysis

The right-hand side of Table 5.2 shows the project`s net present value if the variables are set one at a time to their optimistic and pessimistic values. For example, if fixed costs are $1.9 million rather than the forecast $2.0 million, annual cash flows are increased by (1 tax rate) АГАз ($2.0 million $1.9 million) = .6 АГАз $100,000 = $60,000. If the cash

flow increases by $60,000 a year for 12 years, then the project`s present value increases by $60,000 times the 12-year annuity factor, or $60,000 АГАз 7.536 = $452,000. Therefore, NPV increases from the expected value of $478,000 to $478,000 + $452,000 = $930,000, as shown in the bottom right corner of the table. The other entries in the three columns on the right in Table 5.2 similarly show how the NPV of the project changes when each input is changed.

Your project is by no means a sure thing. The principal uncertainties appear to be sales and variable costs. For example, if sales are only $14 million rather than the forecast $16 million (and all other forecasts are unchanged), then the project has an NPV of $1.218 million. If variable costs are 83 percent of sales (and all other forecasts are unchanged), then the project has an NPV of $788,000.

FIXED COSTS Costs that do not depend on the level of output.

VARIABLE COSTS Costs that change as the level of output changes.

SENSITIVITY ANALYSIS Analysis of the effects on project profitability of changes in sales, costs, and so on.